1. What is the Tilting Angle Formula?

The tilting angle formula calculates the angle formed by a pendulum using the inverse tangent function. It relates the horizontal distance moved to the length of the plumb line in a right triangle configuration.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \theta \) — Tilting angle of body (degrees)
• \( d \) — Distance moved (meters)
• \( l \) — Length of plumb line (meters)

Explanation: The arctangent function calculates the angle whose tangent is the ratio of the opposite side (distance moved) to the adjacent side (length of plumb line) in a right triangle.

3. Importance of Angle Calculation

Details: Accurate angle calculation is crucial for pendulum motion analysis, structural engineering applications, and various mechanical systems where angular displacement needs to be measured.

4. Using the Calculator

Tips: Enter distance moved and length of plumb line in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of possible angles?
A: The angle can range from 0° to 90°, where 0° represents no displacement and 90° represents maximum theoretical displacement.

Q2: How accurate is this calculation?
A: The calculation is mathematically precise for ideal pendulum conditions. Real-world factors like air resistance and friction may cause slight variations.

Q3: Can this formula be used for large angles?
A: While mathematically valid, for pendulum analysis, small angle approximations are often used for angles less than 15° where sinθ ≈ θ.

Q4: What units should be used?
A: Consistent units must be used (both distance and length in meters). The calculator automatically converts the result to degrees.

Q5: Are there limitations to this formula?
A: This formula assumes ideal pendulum conditions and does not account for factors like air resistance, pendulum mass, or non-uniform gravitational fields.